Learning from the uncertain:
Modelling and forecasting of
infectious disease outbreaks

Sebastian Funk
12 December, 2017
Imperial College Bioinformatics

Metcalf & Lessler (Science, 2017)

Forecasting the Ebola epidemic

Summer 2014

\(y=ax+b\)

\begin{eqnarray} \dot{S}&=&-\beta \frac{S}{N}I\\ \dot{I}&=&+\beta \frac{S}{N}I - \gamma I\\ \dot{R}&=&+\gamma I \end{eqnarray}

\(y=ax+b\)

A semi-mechanistic model for real-time forecasting

The unknown

Community/hospital/funeral transmission
Spatial dynamics
Changes in behaviour
Changes in reporting
Interventions
Seasonality
etc

The known

Average incubation period (~9 days)
Average infectious period (~11 days)
Case-fatality rate (~70%)

WHO Ebola response team (NEJM, 2014)

Time-varying transmission rate with smoothing prior

\(d\log \beta_t = \sigma dW_t\)

Dureau et al. (Biostatistics, 2013)

Particle MCMC

Andrieu et al. (J R Stat Soc B, 2010), Dureau et al. (arXiv, 2013), Murray et al. (arXiv, 2013)

\(d\log \beta_t = \sigma dW_t\)
Negative binomial observations, overdispersion \(\phi\)
\(\theta=\{\sigma, \phi, \beta_0, I_0\}\)
- Intensity of random walk
- Overdispersion of reporting
- Initial transmission rate
- Initial number infective

Camacho et al. (PLoS Current, 2015), Funk et al. (Epidemics, 2016)

How good were the forecasts?

"Evaluate predictive performance on the basis of maximising the sharpness of the predictive distribution subject to calibration"

Gneiting et al. (J R Stat Soc B, 2007)

Calibration: Compatibility of forecasts and observations

Cumulative distribution of \(u_t=F_t(x_t)\)

Gneiting et al. (J R Stat Soc B, 2007)

Calibration: Compatibility of forecasts and observations.

Funk et al. (bioRxiv, 2017)

Sharpness: Concentration of predictive distribution

Funk et al. (bioRxiv, 2017)